MASSACHVSETTS INSTITVTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.001--Structure and Interpretation of Computer Programs
Spring Semester, 1999

Recitation - Wednesday, February 3

0. Announcements

• Section Staff:	RI:	Mike Leventon	leventon@ai.mit.edu
  	TA:	Sandia Ren	sren@mit.edu
  	TA:	Hooman Vassef	hvassef@mit.edu	(Half of section 12)

  
  
• Collaboration Policy: Read carefully in the handout.
  
• Attendance: Lecture recommended. Section and Tutorials required.
  
• Problem Sets: No late problem sets accepted. Psets are an important part of your grade. Start them early!
  
• Course Web Page: http://mit.edu/6.001
  
• Section Web Page: http://www.ai.mit.edu/people/leventon/6001
  Section notes (with solutions) will be posted here.

1. Rules for Scheme To evaluate an expression, follow these rules:

• A numeral evaluates to the number
  
• A name evaluates to the value associated with that name
  
• A lambda expression evaluates to a procedure object
  
• A combination is evaulated as follows:
  
  1. Evalute the subexpressions in any order
  2. Apply the value of the operator subexpression to the values of the remaining subexpressions.

To apply a procedure to its arguments, evaluate the body of the procedure where each parameter is replaced by the corresponding value. To evaluate a define, evaluate the body of the define, and associate that value with the name listed in the define.

2. Simple Examples To what do the following expressions evaluate (assume they are evaluated in sequence)?

$\Rightarrow$ 7 ;Value: 7

$\Rightarrow$ - ;Value: #[compiled-procedure ..]

$\Rightarrow$ (+ 2 4) ;Value: 6

$\Rightarrow$ (* (- 5 3) (/ 9 3)) ;Value: 6

$\Rightarrow$ (7 - 4) ;Error: The object 7 is not applicable

3. More Examples To what do the following expressions evaluate (assume they are evaluated in sequence)?

$\Rightarrow$ (lambda (x) (* x x)) ;Value: #[compound-procedure ...] $\Rightarrow$ ((lambda (x) (* x x)) 5) ;Value: 25 $\Rightarrow$ (define double (lambda (x) (* 2 x))) ;Value: "double -> #[compound-procedure ...] $\Rightarrow$ (double (double 6)) ;Value: 24 $\Rightarrow$ (double double) ;Error: #[compound-procedure] passed to multiply

$\Rightarrow$ (define cube (lambda (x) (*x x x))) ;Value: "cube -> #[compound-procedure ...] $\Rightarrow$ (cube 3) ;Error: "Unbound variable: *x" $\Rightarrow$ (define + 3) ;Value: "+ -> 3" $\Rightarrow$ (define - 6) ;Value: "- -> 6" $\Rightarrow$ (* + -) ;Value: 18

4. Writing a Procedure Define a procedure called average that computes the average of its two numeric arguments.

(define average (lambda (x y) (/ (+ x y) 2)))

5. Substitution Model Use the substitution model to evaluate the following expression: (average 4 (double 4))

$\Rightarrow$ ([procedure] 4 (double 4)) $\Rightarrow$ $\Rightarrow$ (double 4) $\Rightarrow$ $\Rightarrow$ ([procedure] 4) $\Rightarrow$ $\Rightarrow$ (* 2 4) $\Rightarrow$ ([procedure] 4 8) $\Rightarrow$ (/ (+ 4 8) 2) $\Rightarrow$ ([procedure /] (+ 4 8) 2) $\Rightarrow$ $\Rightarrow$ (+ 4 8) $\Rightarrow$ ([procedure /] 12 2) $\Rightarrow$ 6

6. Subtleties Consider the following two definitions below. How are they similar and how do they differ?

(define plus +)

(define add (lambda (x y) (+ x y)))

7. More Subtleties What do think should be the values of the following expressions? (Note: these are not things you have to memorize.)

$\Rightarrow$ (+ 4) ;Value: 4 $\Rightarrow$ (- 3) ;Value: -3 $\Rightarrow$ (/ 5) ;Value: 0.2 $\Rightarrow$ (/ 60 5 2 3) ;Value: 2

$\Rightarrow$ (+) ;Value: 0 $\Rightarrow$ (*) ;Value: 1 $\Rightarrow$ (-) ;Error: The procedure #[compiled-procedure] requires at least one argment